%%
%% threeDCFT.tex
%% 
%% Made by Alex Nelson
%% Login   <alex@tomato>
%% 
%% Started on  Sat Aug 29 12:38:56 2009 Alex Nelson
%% Last update Sat Aug 29 12:38:56 2009 Alex Nelson
%%
\documentclass[10pt,oneside]{article}
\usepackage{fly}
\usepackage{brackets}
\usepackage{danger}
\usepackage{float}
%\def\comment#1{}
\title{Calculations in Three Dimensional Chain Field Theory}
\date{August 29, 2009}
%\author{Alex Nelson\\{\tt Email: \href{mailto:pqnelson@gmail.com}{pqnelson@gmail.com}}}
\begin{document}
\maketitle

\section{Notational Warning!}

We will use slightly odd notation for oriented $p+1$ cells
$X_{p+1}$. We will denote it and its orientation in one fell
swoop by
\begin{equation}%\label{eq:}
X_{p+1} = [X_{p} \quad X^{\prime}_{p}]
\end{equation}
as being oriented \emph{from} $X_{p}$ directed \emph{towards} $X^{\prime}_{p}$.
Also we'll use the notation
\begin{equation}%\label{eq:}
e^{-1}_{n}=-e_{n}
\end{equation}
i.e. inverses as such for edges, vertices, faces, $p$-cells, are
actually additive inverses. We can easily deduce how the boundary
operator behaves, since the orientation and boundaries are clearly noted.

\section{The 3-Torus}
\input{tex/torus}
\section{The 3-Sphere}
\input{tex/sphere}

\section{Chain Field Theoretic Calculations}
\input{tex/calc}

\nocite{*}
\bibliographystyle{utcaps}
\bibliography{chain}
\end{document}
